First order operators on shrinking graph-like spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F25%3A00637959" target="_blank" >RIV/61389005:_____/25:00637959 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21340/25:00389375

Výsledek na webu

<a href="https://iopscience.iop.org/article/10.1088/1751-8121/adeb1a" target="_blank" >https://iopscience.iop.org/article/10.1088/1751-8121/adeb1a</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8121/adeb1a" target="_blank" >10.1088/1751-8121/adeb1a</a>

Jazyk výsledku

angličtina

Název v původním jazyce

First order operators on shrinking graph-like spaces

Popis výsledku v původním jazyce

In this article we discuss the convergence of first order operators on a thickened graph (a graph-like space) towards a similar operator on the underlying metric graph. On the graph-like space, the first order operator is of the form exterior derivative (the gradient) on functions and its adjoint (the negative divergence) on closed 1-forms (irrotational vector fields). Under the assumption that each cross section of the tubular edge neighbourhood is convex, that each vertex neighbourhood is simply connected and under suitable uniformity assumptions (which hold in particular, if the space is compact) we establish generalised norm resolvent convergence of the first order operator on the graph-like space towards the one on the metric graph. The square of the first order operator is of Laplace type. On the metric graph, the function (0-form) component is the usual standard (Kirchhoff) Laplacian. A key ingredient in the proof is a uniform Gaffney estimate: such an estimate follows from an equality relating here the divergence operator with all (weak) partial derivatives and a curvature term, together with a (localised) Sobolev trace estimate.

Název v anglickém jazyce

First order operators on shrinking graph-like spaces

Popis výsledku anglicky

In this article we discuss the convergence of first order operators on a thickened graph (a graph-like space) towards a similar operator on the underlying metric graph. On the graph-like space, the first order operator is of the form exterior derivative (the gradient) on functions and its adjoint (the negative divergence) on closed 1-forms (irrotational vector fields). Under the assumption that each cross section of the tubular edge neighbourhood is convex, that each vertex neighbourhood is simply connected and under suitable uniformity assumptions (which hold in particular, if the space is compact) we establish generalised norm resolvent convergence of the first order operator on the graph-like space towards the one on the metric graph. The square of the first order operator is of Laplace type. On the metric graph, the function (0-form) component is the usual standard (Kirchhoff) Laplacian. A key ingredient in the proof is a uniform Gaffney estimate: such an estimate follows from an equality relating here the divergence operator with all (weak) partial derivatives and a curvature term, together with a (localised) Sobolev trace estimate.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Physics A-Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Svazek periodika

58

Číslo periodika v rámci svazku

30

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

31

Strana od-do

305202

Kód UT WoS článku

001536582600001

EID výsledku v databázi Scopus

2-s2.0-10511510039